Tedious details:
— You don't need to draw the board in your solution. Just list the four completed words.
— The spacing dots (·) in the propeller are just there for effect, to represent the underlying structure of the propeller. Their presence or absence does not provide any solving hints.
— There is no rule about the interlacing pattern between the propeller letters and the board letters, just as long as it alternates. It might follow an ABAB pattern, a BABA pattern, an ABABA pattern, or a BABAB pattern.
— Another way of expressing it: The completed word might start with a propeller letter, or it might start with a board letter. It might end with a propeller letter, or it might end with a board letter.
— I tried to craft puzzles with fairly definitive solutions, without too many solution variants. Even so, people are operating from vocabularies of different sizes, and the option to add —s or —d occurs frequently in nature, so we'll have to be somewhat accommodating of solution variants.

1 Answer
1

I've written each "propeller" forward and backward, to make it clearer to see where each word fits.

· S · N · T · R · , · R · T · N · S ·

SANITARY, SENATORS;
RATINGS, PRETENDS

· S · N · B · R · , · R · B · N · S ·

SANDBAR, SONGBIRD;
TRIBUNES, REBINDS

· O · T · R · T · , · T · R · T · O ·

DOCTORATE, POSTERITY;
ITERATION, ATTRITION

· U · E · A · S · , · S · A · E · U ·

NUMERALS, FUNERALS;
SHAMEFUL, STAKEOUT

· N · M · E · E · , · E · E · M · N ·

NUMBERED, UNIMPEDED;
NEVERMIND, REDEEMING

· P · R · E · E · , · E · E · R · P ·

PURVEYED, PARLEYED;
TELEGRAPH, EYEDROPS

· O · T · R · A · , · A · R · T · O ·

OUTBREAK, NOCTURNAL;
NARRATION, AERATION

· S · I · P · E · , · E · P · I · S ·

SKIMPIER, STIPPLED;
DESPAIRS, EMPTIEST

I started out trying to find four words in each direction (filling in diagonals as well as the cardinals), but now I see that it is just two forward and two backward. As such, I believe this answer is complete (edited down to just the required solution).

$\begingroup$Amazingly fast solving! Great work. And thank you for using the classic word "cardinals" to refer to the NESW compass directions. That's exactly how I've been thinking of them.$\endgroup$
– SlowMagicMay 21 '19 at 15:00

$\begingroup$BTW, it's interesting that you were initially thinking of filling in diagonals. I have seen propellers which satisfy 40 different completed words, 20 "forward" and 20 "backward". (As an example, try ·E·I·A·E·) However, these don't seem to make good puzzles because the propeller is too readily apparent from such an overwhelming number of hints, and on the other side, it would simply be too tedious to come up with 40 different completed words for one propeller!$\endgroup$
– SlowMagicMay 21 '19 at 15:01